I don't want "shoes" to trigger my ad, but "black shoes" I do.
That shouldn't ever happen. If it does happen, it's a MAJOR glitch. According to adCenter: "Broad match triggers the display of your ad when individual words in your keyword appear, in any order, in a customer's search query. For example, your keyword "black shoes" would match search queries that include "black shoes," "shoe is black," and other variations, and not just "black" or "shoes."